The Horizontal Spacing of Graphical Notation

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Abstract

While several articles have explored the automated spacing of a line
of music, little attention has been paid to the automated spacing of
graphical notation in the horizontal domain. This article proposes
an algorithm to stretch and compress images so that they are able to
be integrated into a traditional horizontal spacing model while
still attaining certain “target points” in a score. This is done via
a linear program that distributes stretching error over the
graphical object. The linear program is described through a
presentation of its constituent matrices along with several musical
examples that demonstrate its functionality. The article concludes
with ideas regarding the program’s broader applicability to the
domain of graphical notation.